as it might be a grain of millet or of oats or of some similar thing, and that object, if it were larger than the said [black] spot would never be seen as a whole; as may be seen in the diagram below.  Let a. be the seat of sight, b e the lines which reach the eye.  Let e d be the grains of millet within these lines.  You plainly see that these will never diminish by distance, and that the body m n could not be entirely covered by it.  Therefore you must confess that the eye contains within itself one single indivisible point a, to which all the points converge of the pyramid of lines starting from an object, as is shown below.  Let a. b. be the eye; in the centre of it is the point above mentioned.  If the line e f is to enter as an image into so small an opening in the eye, you must confess that the smaller object cannot enter into what is smaller than itself unless it is diminished, and by diminishing it must take the form of a pyramid.

53.

PERSPECTIVE.

Perspective comes in where judgment fails [as to the distance] in objects which diminish.  The eye can never be a true judge for determining with exactitude how near one object is to another which is equal to it [in size], if the top of that other is on the level of the eye which sees them on that side, excepting by means of the vertical plane which is the standard and guide of perspective.  Let n be the eye, e f the vertical plane above mentioned.  Let a b c d be the three divisions, one below the other; if the lines a n and c n are of a given length and the eye n is in the centre, then a b will look as large as b c. c d is lower and farther off from n, therefore it will look smaller.  And the same effect will appear in the three divisions of a face when the eye of the painter who is drawing it is on a level with the eye of the person he is painting.

54.

TO PROVE HOW OBJECTS REACH THE EYE.

If you look at the sun or some other luminous body and then shut your eyes you will see it again inside your eye for a long time.  This is evidence that images enter into the eye.

The relations of the distance points to the vanishing point (55-56).

55.

ELEMENTS OF PERSPECTIVE.

All objects transmit their image to the eye in pyramids, and the nearer to the eye these pyramids are intersected the smaller will the image appear of the objects which cause them.  Therefore, you may intersect the pyramid with a vertical plane [Footnote 4:  Pariete.  Compare the definitions in 85, 2-5, 6-27.  These lines refer exclusively to the third diagram.  For the better understanding of this it should be observed that c s must be regarded as representing the section or profile of a square plane, placed horizontally (comp. lines 11, 14, 17) for which the word pianura is subsequently employed (20, 22).  Lines 6-13 contain certain preliminary observations to guide the reader in understanding the diagram; the last three seem to have been added as a supplement.  Leonardo’s mistake in writing t denota (line 6) for f denota has been rectified.] which reaches the base of the pyramid as is shown in the plane a n.